Based on the recently developed implementation of the full semi-classical field-matter interaction operator, we present a numerically accurate yet efficient scheme to perform rotational averaging of linear absorption spectra beyond the electric-dipole approximation. This allows for a gauge-origin independent determination of UV/vis and X-ray absorption spectra for randomly oriented systems such as multilayers, liquids, and gas phase samples. The approach is illustrated by the determination of spectral intensities of electric-dipole allowed pi -amp;gt; pi* transitions and electric-dipole forbidden n -amp;gt;pi* transitions in the UV-vis region of the spectrum as well as electric-dipole forbidden 1s. 3d transitions in the X-ray region of the spectrum. The employed Lebedev quadrature scheme shows very fast convergence with respect to the number of symmetry-independent quadrature points-in all considered cases, the oscillator strengths for the randomly oriented systems are fully converged with use of only seven quadrature points. [GRAPHICS]